Intensity based models of the portfolio loss process that are specified without reference to the portfolio constituents lead to tractable credit derivatives valuation formulae and accurate tranche market calibrations. We show how to complement these models with random thinning, which decomposes the portfolio loss process into single name loss processes. Random thinning facilitates consistent pricing and calibration of single- and multi-name securities and estimation of single name hedges.

A portfolio credit derivative is a contingent claim on the aggregate loss of a portfolio of credit sensitive securities such as bonds and credit swaps. We propose an affine point process as a dynamic model of portfolio loss. The recovery at each default is random and events are governed by an intensity that is driven by affine jump diffusion risk factors. The portfolio loss itself is a risk factor so past defaults and their recoveries influence future loss dynamics. This specification...

The credit risk premium is empirically documented to be a significant component of credit spreads. However, its determinants are not fully understood. We offer a structural model of the credit risk premium in which investors have incomplete information about a firm's default barrier. The premium has two components. One is standard and accounts for investors' aversion towards price volatility that is due to the diffusive fluctuation of the firm value. The other is an event premium...

In our structural credit model based on incomplete information, investors cannot observe a firm's default barrier.  As a consequence, such a model has both the economic appeal of a structural model and the tractable pricing formulas and empirical plausibility of a reduced-form model.  A comparison of default probability and credit spread forecasts generated by this model and two well-known structural models indicates that it reacts more quickly to new information and, unlike the...

The Modigliani-Miller theorem describes conditions under which the value of a firm is independent of its leverage ratio.  It is one of the cornerstones of finance.  A history of this result along with a modern perspective on its derivation is given in Rubinstein (2003), Journal of Investment Management 1(2).  We extend this history by examining the relationship between the Modigliani-Miller theorem and quantitative models of creditrisk.  In the first part of the paper, we...

The recent string of accounting scandals highlights the need for bond investors to reconsider the informational assumptions underlying traditional models of default. In these models it is implicitly assumed that the information used to calibrate and run the model is publicly available. In reality, model inputs and parameters are uncertain. We develop a class of cause and effect default models based on incomplete information, in which investors can specify the degree of confidence they have...

We develop a structural model of default risk that incorporates the short-term uncertainty inherent in default events. It is based on the assumption of incomplete information: We take as a premise that bond investors are not certain about the true level of firm value that will trigger default. The coherent integration of structure and uncertainty is facilitated with compensators. Compensators form the infrastructure of a class of credit models that is broad enough to include traditional...